Unification of Fusion Rules (UFR)
Florentín Smarandache · viXra · 2004
In this short note we give a formula for the unification of a class of fusion rules based on the conjunctive and/or disjunctive rule at the first step, and afterwards the redistribution of the conflicting and/or non-conflicting mass to the non-empty sets at the second step. Fusion of masses m1(.) and m2(.) is done directly proportional with some parameters and inversely proportional with other parameters (parameters that the hypotheses depend upon). The resulting mass is noted by mUFR(.). a) If variable y is directly proportional with variable p, then y=k1·p, where k1≠0 is a constant. b) If variable y is inversely proportional with variable q, then y=k2·(1/q), where k2≠0 is a constant; we can also say herein that y is directly proportional with variable 1/q. In a general way, we say that if y is directly proportional with variables p1, p2, …, pm and inversely proportionally with variables q1, q2, …, qn, then: y = k·(p1·p2·…·pm)/(q1·q2·…·qn) = k·P/Q, where P= ∏ pi, Q= ∏ qj, and k≠0 is a constant. i= 1 j= 1 With such notations we have a general formula for a UFR rule: mUFR(φ) = 0, and ∀ A∈S Θ \\φ one has: mUFR(A) = d ( X 1 * X 2) T ( X 1, X 2) P(